This task is from Tools for NC Teachers. Students explore the area and perimeter of rectangles using grid (graph) paper. This is remixable.

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Part 1:

Create all the possible arrays with an area of 36 square units.  Draw your arrays on grid paper and label their dimensions.

·       How can you be sure that you found all the possible arrays with an area of 36 square units?

Find the perimeter for each figure that you made.

·       What do you notice about the shapes and their perimeters?

·       What is the relationship between the perimeter and the shape of an array?

Possible Solutions:

  Perimeter     Dimensions

    74 units          1 x 36

    40 units          2 x 18

    30 units          3 x 12

    26 units          4 x 9

    24 units          6 x 6

Part 2:

Create all the possible arrays with a perimeter of 36 units.  Draw your arrays on grid paper and label their dimensions.  Use a chart to keep track of the area and dimensions for each rectangle.

·       How can you be sure that you found all the possible arrays with a perimeter of 36 units?  What do you notice about the shapes and their areas?

·       What is the relationship between the area and the shape of an array?